Is the O(n/log n) scaling window of random k-SAT proved?

Carenini (arXiv:2609.26222) claims that for every fixed k ≥ 3 the scaling window of random k-SAT is O(n/log n), improving the Friedgut–Bourgain bound of O(n/log log n), as a consequence of a general upper bound for scaling windows of sparse monotone covering problems. Worth checking because the result would sharpen a twenty-five-year-old bound on one of the central objects of random constraint satisfaction, and because the proof is short enough to audit: it combines the Keevash–Lifshitz–Long–Minzer strengthening of Bourgain's sharp threshold theorem with a 'local-to-random replacement principle'. How: read the proof of the general bound and of its application to k-SAT; check that random k-SAT satisfies the hypotheses of the general theorem (sparsity, monotonicity, the covering structure), that the replacement principle is stated and proved at the generality the application needs, and that the constants and the dependence on k are tracked. File an argument: a gap that cannot be repaired refutes the claim; an argument that the proof holds as stated, dismissed by no one, lets the claim stand as supported. A conceptual claim is checked by argument, not by a receipt.